(a) Find the slope of the tangent line to the parabola y = x + 8x at the point (-3, -15) by using the following parameters.(i) The tangent line to the curve y =f(x) at the point P(a, f(a)) is the line through P with slopem = limf(x) – f(a)provided that this limit exists.х — аm =f(a + h) – f(a)(ii) The expression of slope is m = limh-0hm =(b) Find an equation of the tangent line in part (a).y =(c) Graph the parabola and the tangent line. As a check on your work, zoom in toward the point (-3, -15) until the parabola and the tangent line are indistinguishable.yy520- 10-55- 10-551010-10-5510-15- 15- 10-20- 20- 20y201010-510- 10- 20

Answered: (a) Find the slope of the tangent line…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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(a) Find the slope of the tangent line to the parabola y = x + 8x at the point (-3, -15) by using the following parameters.
(i) The tangent line to the curve y =
f(x) at the point P(a, f(a)) is the line through P with slopem = lim
f(x) – f(a)
provided that this limit exists.
х — а
m =
f(a + h) – f(a)
(ii) The expression of slope is m = lim
h-0
h
m =
(b) Find an equation of the tangent line in part (a).
y =
(c) Graph the parabola and the tangent line. As a check on your work, zoom in toward the point (-3, -15) until the parabola and the tangent line are indistinguishable.
y
y
5
20
- 10
-5
5
- 10
-5
5
10
10
-10
-5
5
10
-15
- 15
- 10
-20
- 20
- 20
y
20
10
10
-5
10
- 10
- 20

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Step 1

$T h e e q u a t i o n o f t h e p a r a b o l a : y = x^{2} + 8 x T h e \tan g e n t i s a t a p o i n t, A (- 3, - 15) T h e s l o p e o f t h e \tan g e n t a t a n y p o i n t (a, f (a)) m = \lim_{x \to a} \frac{f (x) - f (a)}{x - a} E q u a t i o n o f t h e \tan g e n t p a s \sin g t h r o u g h a, w i t h s l o p e m y - f (a) = m (x - a)$

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